q1: Suppose a? five-year, $1,000 bond with annual coupons has a price of $900.69
ID: 1174668 • Letter: Q
Question
q1:
Suppose a? five-year, $1,000 bond with annual coupons has a price of $900.69 and a yield to maturity of 5.9%. What is the? bond's coupon? rate?
The bound's coupon rate is ??% (round to the three decimal places)
q2:
Suppose that General Motors Acceptance Corporation issued a bond with 10 years until? maturity, a face value of $1,000?, and a coupon rate of 7.2% ?(annual payments). The yield to maturity on this bond when it was issued was 5.9%. What was the price of this bond when it was? issued? (round to the nearest cent.)
Explanation / Answer
1.
Current price=Annual coupons*Present value of annuity factor(5.9%,5)+$1000*Present value of discounting factor(5.9%,5)
900.69=Annual coupons*4.223847908+$1000*0.750792973
900.69=Annual coupons*4.223847908+750.792973
Annual coupon=(900.69-750.792973)/4.223847908
Annual coupon=$35.48826(Approx)
Hence coupon rate=Annual coupon/Face value
=$35.48826/$1000
=3.549%(Approx).
NOTE:
a.Present value of annuity=Annuity[1-(1+interest rate)^-time period]/rate
=Annual coupon[1-(1.059)^-5]/0.059
=Annual coupon*4.223847908
b.Present value of discounting factor=$1000/1.059^5
=$1000*0.750792973
2.
Annual coupon=$1000*7.2%=$72
Hence price when the bond was issued=Annual coupon*Present value of annuity factor(5.9%,10)+$1000*Present value of discounting factor(5.9%,10)
$72*7.395083238+$1000*0.563690088
=$1096.14(Approx).
a.Present value of annuity factor=$72[1-(1.059)^-10]/0.059
=$72*7.395083238
b.Present value of discounting factor=$1000/1.059^10
=$1000*0.563690088
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